Abstract:We investigate the modiﬁed trace distance measure of coherence recently introduced in [Phys. Rev. A 94, 060302(R) (2016)]. We show that for any single-qubit state, the modiﬁed trace norm of coherence is equal to the l1-norm of coherence. For any d-dimensional quantum system, an analytical formula of this measure for a class of maximally coherent mixed states is provided. The trade-oﬀ relation between the coherence quantiﬁed by the new measure and the mixedness quantiﬁed by the trace norm is also discussed. Furthermore, we explore the relation between the modiﬁed trace distance measure of coherence and other measures such as the l1-norm of coherence and the geometric measure of coherence.